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July 26, 2016

This is a random formula I found on fangraphs,
which was NOT used in researching this article!

A series of twitter posts by fans who were convinced that the acquisition of Aroldis Chapman by the Cubs would guarantee them a World Series victory inspired this post.

Fans typically grossly overestimate how much difference a player can make to a team. And there are a couple of reasons why. First of all, just using a basic WAR analysis, you can see that adding a superstar to replace an average player mid-season won’t make a huge difference in the odds of making the playoffs. For example, if you replaced Brock Holt with Mike Trout, based on their current season’s play extrapolated to end of season would give the Red Sox maybe 3 more wins.

If this seems doubtful consider an extreme, but simple case: Red Sox are losing by a run in the World Series in an NL park in extra innings with 2 outs, bases loaded and the pitcher’s spot due up. David Ortiz is on the bench. Should you pinch hit? OF COURSE, everybody knows you should, and it would be an immediately fireable offense for the manager to let the pitcher bat for himself. Assume Ortiz has a 35% chance of getting a hit and winning the game, and the pitcher is batting .150 (for simplicity, assume any hit will be a single that scores 2 runs, ignore walks and errors). How much has pinch hitting increased your chance of winning? Well, 65% of the time, Ortiz is going to make an out just like the pitcher would. Also, 15% of the time the pitcher would get the winning hit just like Ortiz would. It’s only the other 20% of the time that Ortiz will win the game where the pitcher batting wouldn’t. Even in this extreme case, 80% of the time it doesn't matter that you have a better hitter at bat.

But the other thing that fans and analysts often overestimate are the odds of a better team to beat an inferior team in a playoff series. For example, a great 100 win team will beat a "barely made the playoffs" 90 win team only about 56% of the time in asingle
game1. Using some basic math, this works out to them winning 61% of 3 of 5 Series and 63% of the time in a 7 game Series2.
If a team needs to win the LDS, LCS and WS, multiplying out the probabilities works out to under 25% probability that this team will win it all. And that is assuming they get to play “weak” 90 win teams in all the Series.